| Step 1:Initialization: |
| An initial population P is initialized as |
|
| Where , and , V is the uniform |
| distribution function, N is population size, and D is problem |
| dimension. represents chromosome in the population P. |
| and represents the lower limit upper limit of the solution respectively. |
| Step 2: Selection-I: |
| In Selection-I, historical population is determined, |
| which is used to calculate the direction of search for optimum |
| solution. Initial is determined by: |
| . |
| This process is done through the “if-then” rule as: |
|
| Here is defined as update operation, c and d are random |
| numbers in the range which help |
| decide if the Phis is selected from the former generation. |
| After this step the order of the chromosomes is shuffled by |
| random shuffling function given by: |
|
| Step 3: Mutation: |
| A mutation is done in to generate a trail population using: |
|
|
| So, is due to the propagation of chromosomes of in the direction |
| set by ( - ) and G controls amplitude of ( - ). Use of gives a |
| partial advantage to BSA of the experiences of previous |
| population in creating an intelligent trial population . |
| Step 4: Crossover: |
| It creates the final trial population , the |
| initial step towards was set by . Target population is improved |
| by chromosomes of having improved fitness. For this crossover uses two |
| procedures. First determines a binary matrix map of order. Its |
| function is to indicate particles of that are to be changed by using |
| relevant particles of . The initial value of is set as 1, |
| and trial population is updated as: |
|
| Here & . Crossover strategy of |
| BSA is presented in Algorithm 2. BSA uses a unique crossover strategy as |
| compared to other EAs. The mix-rate parameter controls the number of |
| particles that are mutated in atrial by using , is mentioned |
| in line of Algorithm 2. This function is the main reason that BSA crossover |
| is unique to other EAs |
| BSA’s is defined by two predefined strategies being used |
| randomly. The first strategy implements mix-rate (Algorithm 2 |
| line -), and other allows one chromosome to mutate, chosen |
| at random in each trial (Algorithm 2 line -). |
| The mutation strategy results in overflow of some particles of |
| the PT during crossover procedure. For this, a boundary control |
| process is defined that keeps the individual inside the bounds. |
| Its algorithm is given in Algorithm 3. |
| Step 5: Selection-II: |
| In this process the particles of having improved fitness are |
| updated by their corresponding better particles of . The global |
| minimum and global minimizer are also updated based on the best |
| fitness so far. The particle having best fitness is called global |
| minimizer denoted by Pbest and its fitness is called global minimum. |
| Step 6: Termination |
| Finally, optimization process of the BSA is stopped if one the |
| following criterion is met: |
| (i) Max number of iteration is reached, or |
| (ii) The fitness value is below a certain threshold |
